Three-dimensional QED with four-fermion interactions at finite temperature

Using the imaginary-time formalism we derive the temperature-dependent gap equation for the dynamically generated fermion mass of three-dimensional QED with four-fermion interactions. Solving the gap equation numerically, we obtain critical temperatures for several values of N, which is the number of flavors of fermion, of the gauge coupling, and of the four-fermion coupling. We exhibit the diagrams of the relation between mass and temperature.